Given a prime power q, Fq is the type representing elements of the field (eg F4),
fq is a list of the elements of the field, beginning 0,1,... (eg f4),
and for prime power fields, aq is a primitive element, which generates the multiplicative group (eg a4).

The design philosophy is that fq, the list of elements, represents the field.
Thus, many functions elsewhere in the library expect to take fq as an argument,
telling them which field to work over.